## Elementary Geometry for College Students (6th Edition)

The concave kite ( dart ) consists of two congruent triangle with an interior diagonal DB thus $\triangle DBA= \triangle DBC$ by SSS And the interior diagonal BD also bisects angle D and B. measure of $\triangle DBA = measure \triangle DBC= 180^{\circ}$ In $\triangle DBC = \angle C + \angle DBC + \angle CDB = 30+ 15 + \angle DBC = 180$ $Thus \angle DBC= 120$. Same procedure can be follow in the triangle DBC since they are congruent $Thus \angle DBA= 120^{\circ}$ Last step : since the reflex angle $\angle B = \angle DBC + \angle DBA= 240^{\circ}$ Note : since the concave kite or ( dart ) in not a convex polygon its a concave polygon the corollary 2.5.4 cannot be applied on the concave polygon case.
m$\angle$B=360-m$\angle$A-m$\angle$C-m$\angle$D m$\angle$B=360-30-30-30 m$\angle$B=270$^{\circ}$